All astrologers are familiar with the traditional Ptolomaic aspects (conjunction, sextile, square, trine, opposition) and usually the more recently used semi-sextile and quincunx. These are all based on dividing the circle into multiples of two and three, to a total of twelve. Multiples of two are hard aspects, multiples of three, easy ones. They are probably the most popular because they are the easiest to spot using the common 1-30 degree per sign labeling system. But there are also aspects which come from dividing the circle into 5ths, 7ths, 9ths, 11ths, and 13ths, often called “harmonic” aspects because of John Addey’s pioneering work on harmonic charts during the 1970’s which brought these aspects into greater usage. Exactly what they mean and how important they are is still a matter to be decided even among those who use them regularly, so here is a personal approach, based on the theory and structure of the number combinations involved, and sustained by in practice (anecdotal evidence, as some might call experience).
The 5th part of the circle (quintile): 72°, 144°.
This is an aspect with some age and tradition behind it, having been used for quite a while. It is generally associated with natural “talent,” though of what kind is not always made clear. In fact, it has to do with the ability to spot and untilize proportion in either time or space or both. Frequent in the charts of musicians, artists, architects, orators, and others who depend on a good sense of timing or proportion for success. This can be for good or ill, as for instance the chart of Hitler is riddled with 5ths and their halves, 10ths — certainly he was the most talented and compelling orator of the 20th century, and the timing of his decisions was impeccable, despite the way he used it. This quality is likely derived from mathematical applications of the number five itself, from which the Golden Section (phi), is derived. Its formula is:
φ = [√5-1]/2, or 0.6180359...or, magically, φ = [1+√5]/2, or 1.6180359...
and it is the universal proportion of growth within the biological kingdom. It’s the proportion of your elbow to your overall arm, your
naval to your whole frame, seashell and pinecone spiral length and count from level to level, leaf positioning in vines, and so
on. It is much used in all forms of art in architecture, since those are at least in part imitations of life.
The 7th part of the circle (septile): 51°26’, 102°51’.
This aspect is not so much in use, though it has had some popularity. It appears to represent a kind of large-scale, universal outlook on the applications of the planets so attached. It is an ability (indeed, an insistence), to see the Big Picture instead of getting hung up in the details or in only one part of the story. This has a lot of mythological background, as in most Western and much Eastern scripture and secular beliefs, the number seven is associated with completion: the seven days of creation (and thus, the days of the week), the seven heavens, seven archangels, seven pillars of wisdom, seven colors of the rainbow, seven visible planets, seven chakras, seven deadly sins, etc. Even the maximum number of ideas that can be simultaneously held in the brain. It does indeed seem to lend a broad scope of vision in the planetary areas involved in any given horoscope.
The 9th part of the circle (nonile): 40°, 80°, 160° (120° coincides with trine). This aspect is fundamental in Hindu astrology, but peripheral in the West. It is, in my experience, the ultimate “nice person” aspect, of which the quintessential bleeding heart liberal must be entirely constructed. It indicates sympathy, generosity, humanitarianism, and general good will, although it is does not always translate this into assertive action. You want friends? Get some of these...
The 11th part of the circle: 32°44’, 65°27’, 98°11’, 130°55’, 163°38’.
This is a really rough aspect, and wholly unused among traditional astrologers. There is a lot of
Biblical symbolism concerning the number 11 itself, and all of it is
has to do with insufficiency, frustration, and incompletion, a
situation that just falls short of the more whole and complete
number 12. It also seems to be a somewhat
revolutionary number, as it expresses dissatisfaction with the
status quo and fuels a need to overthrow it.
Oddly, in numerology it is called the number of the World
Savior, but that may also have overtones of overthrow.
Remember what Christ did to the money-changers and you may
get a hint. Also His statement, “Think not that I
came to send peace on earth: I came not to send
peace but a sword. For I am come to set a man at
variance with his father, and the daughter against her mother, and
the daughter-in-law against her mother-in-law.” (Matthew
10:34-35). Troublesome stuff – that’s OK if
you’re the Son of God, but hard to handle as a mere
mortal. The Ayatollah Khomeini’s chart was loaded
The 13th part of the
circle: 27°42’. 55°23’, 83°05’, 110°46’, 138°28’,
This is one step beyond
the natural twelve, and folks with a lot of this tend to be one step
beyond, indeed. It is an aspect of the eccentric,
the adventurer, the person who decides to travel the road less taken
or forge out into the woods when the road ends. Sexually, it can be rather kinky (until, of course, kinks
become mainstream, and thus boring), and it may lead to great
adventure or simply to a useless backwater or
cul-de-sac. Some paths are less-traveled for good
reason...but there is always interest and amusement here, if nothing
else, though those traveling in pastures beyond the pale should take
appropriate cautions concerning both the perils of the unknown and
those who don’t feel comfortable with the
Although these are the
main extra fractions of the circle I use for aspects, it would seem
logical to use more, for structural reasons. Although many of the higher, finer aspects are mutual
multiples of larger ones (deciles, for instance, being half of
quintiles), there are still some prime numbers to be reckoned with,
such as 17, 19, 23, 29, 31, and so on. I have
found 17 and 19 to be sort of “upper octaves” of 11 and 13, or at
least similar in some ways. For the rest, seek
out Addey’s work for clues.
Orbs. The question of orbs
for these aspects arises, part of an enduring subject of debate
about all aspects among all astrologers, which opens another
structural problem, but one which is actually easily
solved. If, for instance, we use all fractions of
the circle up to the 36th (ten degrees), and we make the orb for any
two adjacent aspects inversely proportional to their denominators,
we come up with virtually the normal set of orbs for the traditional
aspects most astrologers use — a little under ten degrees max for
an important conjunction, five or six degrees for an opposition,
three or four degrees for a trine or square. But,
using the same formula, some of the finer aspects get wider orbs
than usually in use. A quintile gets 2°, more
than a quincunx is entitled to (about 3/4°), a septile gets a
full 1 1/4°, and so on. Even the unknown 11th is
entitled to more space than a semi-sextile or quincunx.
It would appear that perhaps these somewhat neglected aspects
are more important than they have been given credit for, as we make
the attempt to base our practical usage of astrology on a more
mathematically consistent substrate.
The table above lists all the
fractions of the circle (2-36), with orb limits assigned according
to the size of their denominators (inversely, the smaller the
fraction, the smaller the space it takes up compared with its
neighbor), and it’s interesting to see the patterns they form around
the major aspects. Even though we only go up to the 36th
harmonic here, it’s clear that around the conjunction, opposition,
square, and trine there is a space of infinitely reducing fractional
aspects until the perfect aspect is formed, almost a gravitational
or mathematical swath around the aspects, according to their size.
The little entries really do bow down to the big ones, so it’s no
wonder we favor the traditional aspects. But perhaps we should pay
more attention to the real relative mathematics of nature and take a
closer look at what we have chosen to ignore through the visual
inconvenience of our common 1-30° method of chart
Lagrange Points. Indeed, that image and
model may have more to be said for it, as these same major divisions
of the circle in any planet’s orbit describe its Lagrange points, the attractively stable areas
where other, smaller objects tend to cluster and be ushered along,
like many of the “Trojan” asteroids with Jupiter, many of the
Centaurs with Neptune. Perhaps the very nature of aspects itself is
gravitational, as we are inclined to believe. The bigger the object
and the longer the time it’s been there, the more perfectly aligned
everything else becomes to it, part of the phenomenon of
entrainment. How far that goes down the decreasing scale of
existence, right to our own actions here on earth, is one of the
most important astrological questions to be addressed.
Legrange points: Gravitationally, aspects based on three are stable, others not...is that where astrology gets it from? To play with where these points occur throughout the solar system, plus more nice illustrations and simple math click here.
Copyright: John Townley
Bio: John Townley
Early in his astrological career, John Townley introduced the composite chart technique for analyzing relationships in his book The Composite Chart, and 20 years later wrote the definitive work on the subject, Composite Charts: The Astrology of Relationships. He has pioneered techniques for astrological cycle analysis and proposed a new, physical basis for astrology. He is also the author of Planets in Love, Dynamic Astrology, and Lunar Returns, has been the president of the Astrologers' Guild of America, was the editor of The Astrological Review, and is a contributor to professional and popular astrological magazines. His books have been translated into seven languages.
John is also a well-known journalist, elected member of the American Society of Journalists and Authors, historian, preservationist, performer, and record producer. He can be regularly found, camera and microphone in hand, covering cultural and technological events ranging from the Consumer Electronics Show to the Toy Fair, from international music festivals to ocean sailing races. When he's not behind the camera and microphone, he's in front of them, performing at maritime concerts in the U.S. and across Europe.
Visit Townley's homepage at www.astrococktail.com.